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Circumcentre

If A=6,0,B=0,...

Question

If $A = (6, 0), B = (0, 8),$ and the circumcenter of the $△ O A B$ where $O$ is the origin, is $(α, β),$ then the value of $α + β$ is

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Solution

Point $A$ lies on $x -$ axis
Point $B$ lies on $y -$ axis
$∴ △ O A B$ is right-angled.
Required point is circumcentre which is the mid-point of $A B$ .
$∴ (α, β) = (3, 4) \Rightarrow α + β = 7$

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